A218224 G.f. A(x) satisfies: A(x) = 1+x + x^2*[d/dx A(x)^4].

1, 1, 4, 44, 684, 13636, 328000, 9198240, 294075040, 10549834368, 419626384128, 18330935118080, 872618259925632, 44970631837229184, 2494887017741434368, 148272655438005392896, 9399158287979230003200, 633107847492164526284800, 45159576693655485274008576

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..330

Formula

G.f. A(x) satisfies: A(x) = 1+x + 4*x^2*A(x)^3*A'(x).

a(n) ~ c * 4^n * n! / n^(1/4), where c = 0.2277218505566340305314... - Vaclav Kotesovec, Aug 24 2017

Example

G.f.: A(x) = 1 + x + 4*x^2 + 44*x^3 + 684*x^4 + 13636*x^5 + 328000*x^6 +...
Related series:
A(x)^3 = 1 + 4*x + 22*x^2 + 228*x^3 + 3409*x^4 + 65600*x^5 + 1533040*x^6 +...
d/dx A(x)^3 = 4 + 44*x + 684*x^2 + 13636*x^3 + 328000*x^4 + 9198240*x^5 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x+x^2*deriv(A^4+x*O(x^n))); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A185183, A218223.

Sequence in context: A103870 A371680 A056063 * A177749 A291198 A053332

Adjacent sequences: A218221 A218222 A218223 * A218225 A218226 A218227

Keyword

nonn

Author

Paul D. Hanna, Oct 23 2012

Status

approved